I want to set up a system such that wherever a user of VHF presses the PTT button the coordinates from a GPS receiver will transmited to receiver and stored in a computer. Is that possible ? Where should I look around for something like that?
For transmitting data across a VHF or similar radio link you're going to either need a radio modem or to build one yourself to convert the data bits into tones that can be passed across the link.
While you could, in theory, use an modem device designed for telephone line use (minus the telephone line interface circuitry), a device designed specifically for radio use such as the CMX469A (from CML Microcircuits) would be a much better device, this application note should provide the basis for the system you've described.
FOR LICENSED HAM RADIO AMATEURS ONLY!!
This is what Theran says:
APRS is the solution.
There are several sites to track your APRS position.
Frequencies can be found on the APRS wiki.
Low budged APRS transmitters A Tinytrack is a Terminal Node Controller (TNC) you can couple to almost any modern VHF car transceiver.
Or a microtrack with buld in tinytrack 3 chip.
See the byonics web site.